The topological materials such as topological insulators and Weyl semimetals are inherently characterized by the non-vanishing topological quantum numbers, which are discrete and hence do not permit differential equation for their dynamics. It raises a fundamental issue concerning a possible theoretical framework to describe the dynamics of the topological order. Another unmistakable common feature is that at low energies they are described by Lorentz-invariant relativistic Hamiltonians. A distinctive consequence was recently demonstrated by the length contraction effects on the excitation spectrum in a Lorentz boosted Majorana fermion. This feature makes the topological matters useful test beds for various (special and general) relativistic effects. In this talk, several dynamical setups are investigated, each of which is optimized for the developement of the theoretical dynamics or the relativistic effects in the topological materials.